Question

find the equation of the circle which passes through the point (1,1) and whose centres lie on the y axis at a distance of 6 units from the origin​

Answer 1

Step-by-step explanation:

Let (h,k) be the centre of a circle and its radius is a. Thus, its equation will be (x−h)

2

+(y−k)

2

=a

2

∵ Centre lies on the position direction of y−axis, it x− coordinate will be zero. Hence centre will be (0,y)

And since centre is at a distance 6 from the origin, centre will be (0,6).

And radius (a)=4 is given.

Hence, equation of circle is : (x−0)

2

+(y−6)

2

=4

2

⇒x

2

+y

2

−12y+36=16⇒x

2

+y

2

−12y+20=0

Hence, required equation of circle is,

x

2

+y

2

−12y+20=0